Sturm-Liouville方程奇异边值问题的正解

本文利用不动点指数理论,讨论Sturm-Liouville方程(p(t)u'(t))'+g(t)F(t,u)=0 奇异边值问题的正解的存在性.     

影像变形公式与教材的分歧

把正方体切成无数平行断面,每个断面均有一个光锥,在无数个光锥内观察断面截面与投影截面及断面和断面投影的变化,可得出以下结论：(1)X线影像变形是光锥作用的结果;(2)无论物体投影面是否成角,光锥中心线直射或斜射作用不变;(3)各断面截面的椭圆离心率反映物体空间歪斜程度,是真正的变形因素;(4)投影截面椭圆离心率分别大于、等于或小于断面截面椭圆离心率,则断面正中纵径投影／实长分别大于、等于或小于通过该投影中点的横径投影／实长;(5)若物体投影面成角,将会产生断面投影不均等放大现象;(6)变形程度与物体厚度成正比,且变形的程度与点光源至物体的距离成逆向变化,而与物体投影面距离无关;(7)教材中的论述是错误的。     

Magnetism and magnetoresistance of Er1-xSmxMn6Ge6(x=0.2－1.0) compounds

Magnetic and transport properties of Er_{1-x}Sm_xMn_6Ge_6(x=0.2-1.0) have been investigated by x-ray diffraction (XRD) and magnetization measurement. Analysis of the XRD patterns indicates that the samples with x≤0.4 mainly consist of HfFe_6Ge_6-type phase and the samples with 0.6≤x≤1.0 mainly consist of YCo_6Ge_6-type phase (P6/mmm). The lattice constants and the unit cell volume increase with increasing Sm content. The antiferro－ferri－ferromagnetic transitions can be observed with increasing Sm content. The samples with x=0.2 and 0.4 order antiferromagnetically at 420 and 425K, respectively. The samples with x=0.6, 0.8 and 1.0 order from ferri- to ferromagnetically over the whole magnetic ordering temperature range. The corresponding Curie temperatures are 435, 441 and 446K, respectively. The magnetoresistance (MR) isotherms of the sample with x=0.8, measured at various temperatures, are analysed. The magnitude of MR is found to be positive below 55K and gradually increases to a relatively large value of about 5.02% at 5K in a field of 5T as the temperature is lowered. A possible explanation for the positive MR is given.     

任意四边形网格上解辐射输运方程的一种数值方法

解二维辐射输运问题时,对于矩形网格,用Sn菱形(diamond)格式处理十分简单有效,但该格式不能直接用于非矩形网格,而辐射流体力学计算往往要求在非矩形网格上进行.本文讨论任意四边形网格的辐射输运数值方法,给出一种全正的子网格平衡计算格式,并进行数值计算,与矩形网格Sn菱形格式结果比较,得出本方法可行性结论.     

${mbox{boldmath $R$}}^N$上奇异非线性多调和方程的正整体解

本文研究形如△((△nu)(p-1) )=f(|x|,u,|(?)u|)u-β,x∈RN的奇异非线性多调和方程在RN上的正整体解,此处P>1,β≥0是常数,n是自然数,f:R × R ×R →R 是一个连续函数, ξδ*:=sign(ξ)·|ξ|δ,,ξ∈R,δ>0,给出了该类方程具有无穷多个其渐进阶刚好为|x|2n的正整体解的充分条件与必要条件.这些结论可以推广到更一般的方程.     

非共振奇异超线性边值问题正解存在的充分必要条件

本文研究非共振奇异超线性边值问题正解的存在性,利用锥上的不动点定理给出了非共振奇异超线性边值问题有C1[0,1]正解存在的充分必要条件.     

二阶拟线性微分方程组边值问题的三个对称正解

本文讨论二阶拟线性微分方程组边值问题( p(x'))'+a(t),(t,x,y)=0,( q(y'))'+b(t)g(t,x,y)=0,x(0)-B0(x'(0))=x(1)+Bo(x'(1))=0,y(0)-B1(y'(0))=y(1)+B1(y'(1))=0,其中f,g是非负连续的函数.利用五个泛函的不动点定理,赋予f和g一些增长条件保证至少三个对称正解的存在性.